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All sourcesNASA NTRSDOE OSTI
NASA NTRS2023

Towards Soil Moisture Profile Estimation in the Root Zone Using L- and P-Band Radiometer Observations: A Coherent Modelling Approach

Precision irrigation management and crop water stress assessment rely on accurate estimation of root zone soil moisture. However, only the top 5cm soil moisture can be estimated using the two current passive microwave satellite missions, Soil Moisture and Ocean Salinity (SMOS) and Soil Moisture Active Passive (SMAP), which operate at L-band (wavelength of ~21cm). Since the contributing depth of the soil to brightness temperature increases with observation wavelength, it is expected that a P-band (wavelength of ~40cm) radiometer could potentially provide soil moisture information from deeper layers of the soil profile. Moreover, by combining both L- and P- bands, it is hypothesized that the soil moisture profile can be estimated even beyond their individual observation depths. The aim of this study was to demonstrate the potential of combined L-band and P-band radiometer observations to estimate the soil moisture profile under flat bare soil using a stratified coherent forward model. Brightness temperature observations at L-band and P-band from a tower based experimental site across a dry (April 2019) and a wet (March 2020) period, covering different soil moisture profile shapes, were used in this study. Results from an initial synthetic study showed that the performance of a combined L-band and P-band approach was better than the performance of using either band individually, with an average depth over which reliable soil moisture profile information could be estimated (i.e. with a target root mean square error (RMSE) of less than 0.04 m3/m3) being 20cm for linear and 15cm for second-order polynomial functions. Other functions were also tested but found to have a poorer performance. Applying the method to the tower-based brightness temperature achieved an average estimation depth of 28cm (20cm) and 5cm (5cm) during the dry and wet periods respectively when using a second-order polynomial (linear) function. These findings highlight the opportunity of a satellite mission with L-band and P-band observations to accurately estimate the soil moisture profile to as deep as 30cm globally.

Foad Brakhasi↗
NASA NTRSDate not supplied

Is There A Relationship Between Cornered-Hat Methods and A Residual Approach to Estimate System Uncertainty?

Recently a relationship has been established between a now traditional residual diagnostic used to estimate observation, background and analysis error covariances of interest to data assimilation and the three-cornered hat (3CH) method. An existing extension of the traditional residual diagnostic uses residuals from a fixed lag-1 Kalman smoother to retrieve system (model) error covariance. It is thus natural to ask if an additional relationship can be established between this extended residual method and some form of cornered--hat method. The answer might seem straightforward. Unlike in the standard residual estimation case, attempting to estimate model error amounts to estimating the statistics of a residual quantity itself. As shown in this presentation, in such cases the 3CH method becomes trivial: the sought out uncertainty can be derived directly from the covariance of the residual quantity at hand. In the particular case of estimating model error, one of the corners would have to be composed of vectors providing estimates of model error; these are not typically available in practice. Therefore, at first glance the present work finds no relationship between the lag-1 smoother residual diagnostic for system error estimation and cornered--hat methods. However, the work suggests that a two-tiered 3CH might be all that is necessary for system uncertainty to be obtained with 3CH.

Ricardo Todling↗
NASA NTRS2023

A Hyperspectral Inversion Framework for Estimating Absorbing Inherent Optical Properties and Biogeochemical Parameters in Inland and Coastal Waters

The simultaneous remote estimation of biogeochemical parameters (BPs) and inherent optical properties (IOPs) from hyperspectral satellite imagery of globally distributed optically distinct inland and coastal waters is a complex, unsolved, non-unique inverse problem. To tackle this problem, we leverage a machine-learning model termed Mixture Density Networks (MDNs). MDNs outperform operational algorithms by calculating the covariance between the simultaneously estimated products. We train the MDNs on a large ( N = 8237) dataset of co-aligned, in situ measured, hyperspectral remote sensing reflectance (R rs ), BPs, and absorbing IOPs from globally representative optically distinct inland and coastal waters. The estimated IOPs include absorption due to phytoplankton (a ph ), chromophoric dissolved organic matter (a cdom ), and non-algal particles (a nap ). The estimated BPs include chlorophyll-a, total suspended solids, and phycocyanin (PC). MDNs dramatically reduce uncertainty in the retrievals, relative to operational algorithms, when using a 50/50 dataset split, where the MDNs are trained on a randomly selected half of the in situ dataset and validated on the other half. Our model is shown to have higher, or equivalent, generalization performance than the calculated operational algorithms available for all BPs and IOPs (except PC) via a leave-one-out cross-validation assessment. The MDNs are sensitive to uncertainties in the hyperspectral satellite R rs , resulting from instrument noise and atmospheric correction; there is a difference of ~37.4–62.8% (using median symmetric accuracy) between the MDNs’ estimates derived from co-located satellite-derived R rs and in situ R rs . Of the IOPs, a cdom and a nap are less sensitive to uncertainties in hyperspectral satellite imagery relative to a ph , with remote estimates of a ph exhibiting incorrect spectral shape and magnitude relative to in situ measured IOPs. Despite the uncertainties in satellite derived R rs , the spatial distributions of BPs and IOPs in MDN-derived product maps of Lake Erie and the Curonian Lagoon, based on imagery taken with the Hyperspectral Imager for the Coastal Ocean (HICO) and PRecursore Iper-Spettrale della Missione Applicativa (PRISMA), are confirmed via co-aligned in situ measurements and agree with the literature’s understanding of these well-studied regions. The consistency and accuracy of the model on HICO and PRISMA imagery, despite radiometric uncertainties, demonstrate its applicability to future hyperspectral missions, such as the Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission, where the simultaneous estimation model will serve as a key part of phytoplankton community composition analysis.

Ryan E. O'Shea↗
DOE OSTI2012

State estimation of an acid gas removal (AGR) plant as part of an integrated gasification combined cycle (IGCC) plant with CO2 capture

An accurate estimation of process state variables not only can increase the effectiveness and reliability of process measurement technology, but can also enhance plant efficiency, improve control system performance, and increase plant availability. Future integrated gasification combined cycle (IGCC) power plants with CO2 capture will have to satisfy stricter operational and environmental constraints. To operate the IGCC plant without violating stringent environmental emission standards requires accurate estimation of the relevant process state variables, outputs, and disturbances. Unfortunately, a number of these process variables cannot be measured at all, while some of them can be measured, but with low precision, low reliability, or low signal-to-noise ratio. As a result, accurate estimation of the process variables is of great importance to avoid the inherent difficulties associated with the inaccuracy of the data. Motivated by this, the current paper focuses on the state estimation of an acid gas removal (AGR) process as part of an IGCC plant with CO2 capture. This process has extensive heat and mass integration and therefore is very suitable for testing the efficiency of the designed estimators in the presence of complex interactions between process variables. The traditional Kalman filter (KF) (Kalman, 1960) algorithm has been used as a state estimator which resembles that of a predictor-corrector algorithm for solving numerical problems. In traditional KF implementation, good guesses for the process noise covariance matrix (Q) and the measurement noise covariance matrix (R) are required to obtain satisfactory filter performance. However, in the real world, these matrices are unknown and it is difficult to generate good guesses for them. In this paper, use of an adaptive KF will be presented that adapts Q and R at every time step of the algorithm. Results show that very accurate estimations of the desired process states, outputs or disturbances can be achieved by using the adaptive KF.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Method and system to estimate variables in an integrated gasification combined cycle (IGCC) plant

System and method to estimate variables in an integrated gasification combined cycle (IGCC) plant are provided. The system includes a sensor suite to measure respective plant input and output variables. An extended Kalman filter (EKF) receives sensed plant input variables and includes a dynamic model to generate a plurality of plant state estimates and a covariance matrix for the state estimates. A preemptive-constraining processor is configured to preemptively constrain the state estimates and covariance matrix to be free of constraint violations. A measurement-correction processor may be configured to correct constrained state estimates and a constrained covariance matrix based on processing of sensed plant output variables. The measurement-correction processor is coupled to update the dynamic model with corrected state estimates and a corrected covariance matrix. The updated dynamic model may be configured to estimate values for at least one plant variable not originally sensed by the sensor suite.

47 OTHER INSTRUMENTATION↗
DOE OSTI2014

Performance Bounds on Micro-Doppler Estimation and Adaptive Waveform Design Using OFDM Signals

We analyze the performance of a wideband orthogonal frequency division multiplexing (OFDM) signal in estimating the micro-Doppler frequency of a target having multiple rotating scatterers (e.g., rotor blades of a helicopter, propellers of a submarine). The presence of rotating scatterers introduces Doppler frequency modulation in the received signal by generating sidebands about the transmitted frequencies. This is called the micro-Doppler effects. The use of a frequency-diverse OFDM signal in this context enables us to independently analyze the micro-Doppler characteristics with respect to a set of orthogonal subcarrier frequencies. Therefore, to characterize the accuracy of micro-Doppler frequency estimation, we compute the Cram er-Rao Bound (CRB) on the angular-velocity estimate of the target while considering the scatterer responses as deterministic but unknown nuisance parameters. Additionally, to improve the accuracy of the estimation procedure, we formulate and solve an optimization problem by minimizing the CRB on the angular-velocity estimate with respect to the transmitting OFDM spectral coefficients. We present several numerical examples to demonstrate the CRB variations at different values of the signal-to-noise ratio (SNR) and the number of OFDM subcarriers. The CRB values not only decrease with the increase in the SNR values, but also reduce as we increase the number of subcarriers implying the significance of frequency-diverse OFDM waveforms. The improvement in estimation accuracy due to the adaptive waveform design is also numerically analyzed. Interestingly, we find that the relative decrease in the CRBs on the angular-velocity estimate is more pronounced for larger number of OFDM subcarriers.

Sen, Satyabrata↗
DOE OSTI2019

Sensor Error Estimation for Reactor Coolant System with Generalization Error Equations

We consider a simplified version of the sensor error estimation problem in pressure sensors in the primary coolant system of a nuclear power plant under the condition that a majority of sensors are error-free. We present a sensor fusion method to estimate sensor errors in the primary coolant system of a power reactor by using measurements collected by multiple sensors. The underlying relationship between the measured and estimated parameters is inferred using measurements collected under controlled no-error conditions of the plant. We propose a machine learning approach to train fusers that provide an estimate of the sensor measurement by using measurements from other sensors, and the difference between the actual sensor measurement and its estimate provides the sensor estimate. We present generalization error equations for these methods that characterize the performance of their sensor error estimates on future measurements using the distribution-free machine learning formulation.

Rao, Nageswara S.↗
DOE OSTI2020

Ambient Synchrophasor Measurement Based System Inertia Estimation

This paper develops an algorithm to estimate the system inertia value based on ambient synchrophasor measurement. Informative features are extracted from ambient synchrophasor measurements for machine-learning-based inertia estimation. Besides ambient synchrophasor measurements of FNET/GridEye, other available data relevant to inertia (such as weather and system load data) are also used to improve the inertia estimation accuracy. Then a machine learning algorithm to estimate system inertia is developed. A test dataset including ambient synchrophasor data from FNET/GridEye measurements and the WECC system inertia data from NERC is used to evaluate the performance of the developed inertia estimation method. The average and maximum estimation errors of the developed inertia estimation method is lower than 5% and 10%, respectively. This accuracy is higher than reported accuracy values in existing literature.

CUI, YI↗
DOE OSTI2013

Comparison of Statistically Modeled Contaminated Soil Volume Estimates and Actual Excavation Volumes at the Maywood FUSRAP Site - 13555

As part of the ongoing remediation process at the Maywood Formerly Utilized Sites Remedial Action Program (FUSRAP) properties, Argonne National Laboratory (Argonne) assisted the U.S. Army Corps of Engineers (USACE) New York District by providing contaminated soil volume estimates for the main site area, much of which is fully or partially remediated. As part of the volume estimation process, an initial conceptual site model (ICSM) was prepared for the entire site that captured existing information (with the exception of soil sampling results) pertinent to the possible location of surface and subsurface contamination above cleanup requirements. This ICSM was based on historical anecdotal information, aerial photographs, and the logs from several hundred soil cores that identified the depth of fill material and the depth to bedrock under the site. Specialized geostatistical software developed by Argonne was used to update the ICSM with historical sampling results and down-hole gamma survey information for hundreds of soil core locations. The updating process yielded both a best guess estimate of contamination volumes and a conservative upper bound on the volume estimate that reflected the estimate's uncertainty. Comparison of model results to actual removed soil volumes was conducted on a parcel-by-parcel basis. Where sampling data density was adequate, the actual volume matched the model's average or best guess results. Where contamination was un-characterized and unknown to the model, the actual volume exceeded the model's conservative estimate. Factors affecting volume estimation were identified to assist in planning further excavations. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2012

Estimate of the Potential Amount of Low-Level Waste from the Fukushima Prefecture - 12370

The amount of waste generated by the cleanup of the Fukushima Prefecture (Fukushima-ken) following the releases from the Fukushima Daiichi nuclear power plant accident (March 2011) is dependent on many factors, including: - Contamination amounts; - Cleanup levels determined for the radioisotopes contaminating the area; - Future land use expectations and human exposure scenarios; - Groundwater contamination considerations; - Costs and availability of storage areas, and eventually disposal areas for the waste; and - Decontamination and volume reduction techniques and technologies used. For the purposes of estimating these waste volumes, Fukushima-ken is segregated into zones of similar contamination level and expected future use. Techniques for selecting the appropriate cleanup methods for each area are shown in a decision tree format. This approach is broadly applied to the 20 km evacuation zone and the total amounts and types of waste are estimated; waste resulting from cleanup efforts outside of the evacuation zone is not considered. Some of the limits of future use and potential zones where residents must be excluded within the prefecture are also described. The size and design of the proposed intermediate storage facility is also discussed and the current situation, cleanup, waste handling, and waste storage issues in Japan are described. The method for estimating waste amounts outlined above illustrates the large amount of waste that could potentially be generated by remediation of the 20 km evacuation zone (619 km{sup 2} total) if the currently proposed cleanup goals are uniformly applied. The Japanese environment ministry estimated in early October that the 1 mSv/year exposure goal would make the government responsible for decontaminating about 8,000 km{sup 2} within Fukushima-ken and roughly 4,900 km{sup 2} in areas outside the prefecture. The described waste volume estimation method also does not give any consideration to areas with localized hot spots. Land use and area dose rate estimates for the 20 km evacuation zone indicate there are large areas where doses to the public can be mitigated through methods other than removal and disposal of soil and other wastes. Several additional options for waste reduction can also be considered, including: - Recycling/reusing or disposing of as municipal waste material that can be unconditionally cleared; - Establishing additional precautionary (e.g., liners) and monitoring requirements for municipal landfills to dispose of some conditionally-cleared material; and - Using slightly-contaminated material in construction of reclamations, banks and roads. Waste estimates for cleanup will continue to evolve as decontamination plans are drafted and finalized. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2019

Resilient Distributed Parameter Estimation With Heterogeneous Data

This paper studies resilient distributed estimation under measurement attacks. A set of agents each makes successive local, linear, noisy measurements of an unknown vector field collected in a vector parameter. The local measurement models are heterogeneous across agents and may be locally unobservable for the unknown parameter. An adversary compromises some of the measurement streams and changes their values arbitrarily. The agents' goal is to cooperate over a peer-to-peer communication network to process their (possibly compromised) local measurements and estimate the value of the unknown vector parameter. We present SAGE, the Saturating Adaptive Gain Estimator, a distributed, recursive, consensus + innovations estimator that is resilient to measurement attacks. We demonstrate that, as long as the number of compromised measurement streams is below a particular bound, then, SAGE guarantees that all of the agents' local estimates converge almost surely to the value of the parameter. The resilience of the estimator - i.e., the number of compromised measurement streams it can tolerate - does not depend on the topology of the inter-agent communication network. Finally, we illustrate the performance of SAGE through numerical examples.

42 ENGINEERING↗
DOE OSTI2012

Fourier domain closed-form formulas for estimation of kinetic parameters in reversible multi-compartment models

Background: Compared with static imaging, dynamic emission computed tomographic imaging with compartment modeling can quantify in vivo physiologic processes, providing useful information about molecular disease processes. Dynamic imaging involves estimation of kinetic rate parameters. For multi-compartment models, kinetic parameter estimation can be computationally demanding and problematic with local minima. Methods: This paper offers a new perspective to the compartment model fitting problem where Fourier linear system theory is applied to derive closed-form formulas for estimating kinetic parameters for the two-compartment model. The proposed Fourier domain estimation method provides a unique solution, and offers very different noise response as compared to traditional non-linear chi-squared minimization techniques. Results: The unique feature of the proposed Fourier domain method is that only low frequency components are used for kinetic parameter estimation, where the DC (i.e., the zero frequency) component in the data is treated as the most important information, and high frequency components that tend to be corrupted by statistical noise are discarded. Computer simulations show that the proposed method is robust without having to specify the initial condition. The resultant solution can be fine tuned using the traditional iterative method. Conclusions: The proposed Fourier-domain estimation method has closed-form formulas. The proposed Fourier-domain curve-fitting method does not require an initial condition, it minimizes a quadratic objective function and a closed-form solution can be obtained. The noise is easier to control, simply by discarding the high frequency components, and emphasizing the DC component.

Nuclear medicine imaging↗
DOE OSTI2021

The XFaster Power Spectrum and Likelihood Estimator for the Analysis of Cosmic Microwave Background Maps

We present the XFaster analysis package, XFaster is a fast, iterative angular power spectrum estimator based on a diagonal approximation to the quadratic Fisher matrix estimator. XFaster uses Monte Carlo simulations to compute noise biases and filter transfer functions and is thus a hybrid of both Monte Carlo and quadratic estimator methods. In contrast to conventional pseudo-C ℓ based methods, the algorithm described here requires a minimal number of simulations, and does not require them to be precisely representative of the data to estimate accurate covariance matrices for the bandpowers. The formalism works with polarization-sensitive observations and also data sets with identical, partially overlapping, or independent survey regions. The method was first implemented for the analysis of BOOMERanG data (Netterfield et al. 2002; Jones et al. 2006), and also used as part of the Planck analysis (Rocha et al. 2011). Here, we describe the full, publicly available analysis package, written in Python, as developed for the analysis of data from the 2015 flight of the SPIDER instrument (SPIDER Collaboration 2021). The package includes extensions for self-consistently estimating null spectra and for estimating fits for Galactic foreground contributions. We show results from the extensive validation of XFaster using simulations, and its application to the SPIDER data set.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2015

Total Land Water Storage Change over 2003 - 2013 Estimated from a Global Mass Budget Approach

We estimate the total land water storage (LWS) change between 2003 and 2013 using a global water mass budget approach. Hereby we compare the ocean mass change (estimated from GRACE space gravimetry on the one hand, and from the satellite altimetry-based global mean sea level corrected for steric effects on the other hand) to the sum of the main water mass components of the climate system: glaciers, Greenland and Antarctica ice sheets, atmospheric water and LWS (the latter being the unknown quantity to be estimated). For glaciers and ice sheets, we use published estimates of ice mass trends based on various types of observations covering different time spans between 2003 and 2013. From the mass budget equation, we derive a net LWS trend over the study period. The mean trend amounts to +0.30 +/- 0.18 mm/yr in sea level equivalent. This corresponds to a net decrease of −108 +/- 64 cu km/yr in LWS over the 2003-2013 decade. We also estimate the rate of change in LWS and find no significant acceleration over the study period. The computed mean global LWS trend over the study period is shown to be explained mainly by direct anthropogenic effects on land hydrology, i.e. the net effect of groundwater depletion and impoundment of water in man-made reservoirs, and to a lesser extent the effect of naturally-forced land hydrology variability. Our results compare well with independent estimates of human-induced changes in global land hydrology.

Water↗
DOE OSTI2016

Sequential ensemble-based optimal design for parameter estimation

The ensemble Kalman filter (EnKF) has been widely used in parameter estimation for hydrological models. The focus of most previous studies was to develop more efficient analysis (estimation) algorithms. On the other hand, it is intuitively understandable that a well-designed sampling (data-collection) strategy should provide more informative measurements and subsequently improve the parameter estimation. In this work, a Sequential Ensemble-based Optimal Design (SEOD) method, coupled with EnKF, information theory and sequential optimal design, is proposed to improve the performance of parameter estimation. Based on the first-order and second-order statistics, different information metrics including the Shannon entropy difference (SD), degrees of freedom for signal (DFS) and relative entropy (RE) are used to design the optimal sampling strategy, respectively. The effectiveness of the proposed method is illustrated by synthetic one-dimensional and two-dimensional unsaturated flow case studies. It is shown that the designed sampling strategies can provide more accurate parameter estimation and state prediction compared with conventional sampling strategies. Optimal sampling designs based on various information metrics perform similarly in our cases. Furthermore, the effect of ensemble size on the optimal design is also investigated. Overall, larger ensemble size improves the parameter estimation and convergence of optimal sampling strategy. Although the proposed method is applied to unsaturated flow problems in this study, it can be equally applied in any other hydrological problems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Estimating traffic volumes for signalized intersections using connected vehicle data

Recently connected vehicle (CV) technology has received significant attention thanks to active pilot deployments supported by the US Department of Transportation (USDOT). At signalized intersections, CVs may serve as mobile sensors, providing opportunities of reducing dependencies on conventional vehicle detectors for signal operation. However, most of the existing studies mainly focus on scenarios that penetration rates of CVs reach certain level, e.g., 25%, which may not be feasible in the near future. How to utilize data from a small number of CVs to improve traffic signal operation remains an open question. In this work, we develop an approach to estimate traffic volume, a key input to many signal optimization algorithms, using GPS trajectory data from CV or navigation devices under low market penetration rates. To estimate traffic volumes, we model in this paper vehicle arrivals at signalized intersections as a time-dependent Poisson process, which can account for signal coordination. The estimation problem is formulated as a maximum likelihood problem given multiple observed trajectories from CVs approaching to the intersection. An expectation maximization (EM) procedure is derived to solve the estimation problem. Two case studies were conducted to validate our estimation algorithm. One uses the CV data from the Safety Pilot Model Deployment (SPMD) project, in which around 2800 CVs were deployed in the City of Ann Arbor, MI. The other uses vehicle trajectory data from users of a commercial navigation service in China. Mean absolute percentage error (MAPE) of the estimation is found to be 9–12%, based on benchmark data manually collected and data from loop detectors. Finally, considering the existing scale of CV deployments, the proposed approach could be of significant help to traffic management agencies for evaluating and operating traffic signals, paving the way of using CVs for detector-free signal operation in the future.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Estimating and Forecasting Time-Varying Groundwater Recharge in Fractured Rock: A State-Space Formulation with Preferential and Diffuse Flow to the Water Table

Rapid infiltration following precipitation may result in groundwater contamination from surface contaminants or pathogens. In fractured rock, contaminants can migrate rapidly to points of groundwater withdrawals. In contrast to the temporal availability of groundwater quality chemical indicators, meteorological and groundwater level observations are available in real-time to estimate time-varying recharge, which can act as a surrogate to identify periods of rapid infiltration that may indicate contamination susceptibility. Estimating recharge using methods, such as base-flow recession, unsaturated infiltration models, or Water-Table Fluctuations (WTF), cannot capitalize on currently available technologies and telecommunication infrastructure to conduct real-time recharge estimation at scales relevant to characterizing rapid infiltration. We present a linear, physics-based State-Space (SS) model of one-dimensional infiltration to estimate recharge, which includes preferential and diffuse-flow to the water table. The model can take advantage of real-time data for water-table altitude, precipitation, and evapotranspiration. Model parameters are calibrated over an observation period, and the Kalman Filter (KF) is subsequently applied to continuously update the observed (water-table altitude) and unobserved (groundwater recharge) system states and predict future states as new data become available. The SS/KF algorithm is demonstrated at the Masser Groundwater Recharge Site in Pennsylvania, USA and comparisons are made with recharge estimates from WTF methods. Model results indicate that the frequency of observations (daily versus sub-daily) dictates the allocation between preferential and diffuse flow. Additionally, because infiltration processes encompass many nonlinearities, model parameters estimated from observation periods need to be updated at least seasonally to account for changing recharge conditions.

groundwater, Recharge, infiltration, recursive est↗
DOE OSTI2017

Neutron Multiplicity Counting Moments for Fissile Mass Estimation in Scatter-Based Neutron Detection Systems

Neutron multiplicity counting (NMC) techniques are widely used for nuclear materials accountability and international safeguards applications to quantitatively evaluate characteristic properties pertaining to fissile material. Mathematical models for NMC moments have been previously derived for systems that use capture-based detectors; however, these models are not applicable when scatter-based detectors are used because of “neutron cross talk.” Neutron cross talk occurs when a single neutron scatters and deposits energy above threshold into multiple detectors causing spurious increase in multiplicity counts; this, in turn, has caused fissile mass to be overestimated when not treated. In this paper, we propose new mathematical models derived from point kinetics to correct for neutron cross-talk effects up to any arbitrary order N, where N denotes the maximum number of counts a single neutron can cause. The new models were used to estimate the fissile mass of plutonium metal and oxide samples with effective 240 Pu mass ranging from 2.5 to 250 g. The adequacy of the models was confirmed using simulations of a conceptual scatter-based neutron multiplicity counter (e.g., organic scintillators) using MCNPX v2.7e with the PoliMi fission event generating extension. The fissile mass estimates with no correction for neutron cross-talk events yielded an average relative deviation from the true 240 Pu eff mass of 55.94% and 84.56% for metal and oxide samples, respectively. When neutron cross-talk events of order N = 2 are included in the model, the fissile mass estimates yielded an average relative deviation of 11.89% for metal and 13.21% for oxide samples. Accounting for neutron cross-talk events of order N = 3 resulted in fissile mass estimates with an average relative deviation of 9.58% and 10.51% for metal and oxide samples, respectively. These mass estimates were compared to a reference case (i.e., no neutron crosstalk effects) that yielded an average relative deviation of 6.81% and 4.77% for metal and oxide samples, respectively. In conclusion, the discrepancy between the estimates from the proposed model and the reference case is attributed to the assumed value of N, which sets a finite upper bound on the order of cross-talk events the model treats (i.e., the model for N = 3 assumes that a neutron will never cause more than three counts).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗